Abstract
Abstract Whether or not dark energy evolves with time may be determined by the nonparametric method. In order to avoid instability of the derivative for the functional data, we linearize the luminosity-distance integral formula in near-flat space by adopting Lagrange interpolation for the numerical integral, and proposing a method of combining principal component analysis (PCA) and biased estimation on the basis of ridge regression analysis to reconstruct the regression parameters. We also present a principal component selection criterion to better distinguish between ΛCDM and w(z) ≠ −1 models by reconstruction. We define the type I error as the situation where w true = −1 but w recon ≠ −1, and the type II error as the situation where w true ≠ −1 but w recon = −1; we use the various w(z) functions to test the method. The preliminary test results demonstrate that the PCA-biased method can be used to determine the most probable behavior of w(z). Finally, we apply this method to recent supernova measurements, reconstructing the continuous history of w(z) out to redshift z = 1.5.
Highlights
Since the cosmic acceleration was firstly discovered in 1998 (Riess et al 1998), physicists predict the existence of dark energy for explaining the accelerating expansion of the universe, on the other hand, the nature of dark energy whether or not evolves with time has become a significant issue (Linder et al 2003)
Hubble parameters including some data obtained from the age-redshift relationship of galaxies can be directly used to reconstruct the dark energy w(z) models because its correction does not need to depend on a prior cosmological model (Riess et al 2002)
We propose a new principal component selection criterion to better distinguish between ΛCDM and w(z) = −1 models by reconstruction
Summary
Since the cosmic acceleration was firstly discovered in 1998 (Riess et al 1998), physicists predict the existence of dark energy for explaining the accelerating expansion of the universe, on the other hand, the nature of dark energy whether or not evolves with time has become a significant issue (Linder et al 2003). Hubble parameters including some data obtained from the age-redshift relationship of galaxies can be directly used to reconstruct the dark energy w(z) models because its correction does not need to depend on a prior cosmological model (Riess et al 2002). Original observation data including Type Ia SNe, Hubble parameter H(z), cosmic microwave background radiation(CMB), and large scale structure (LSS) can be employed to obtain statistical results to measure the dynamic property of dark energy. Iii) PCA with the smoothness prior (Riess et al 2009; Crittenden et al 2012; Zhao et al 2012), the results obtained by this method are good, considering that it is a non-linear regression, the calculation is more complicated, and the choice of principal components and the covariance function parameters have the above problems.
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